Question

Read the following statement :

An equilateral triangle is a polygon made up of three line segments out of which two line segments are equal to the third one and all its angles are 60° each.
Define the terms used in this definition which you feel necessary. Are there any undefined terms in this? Can you justify that all sides and all angles are equal in a equilateral triangle.

Answer 1

The terms need to be defined are

1. Polygon: A closed figure bounded by three or more line segments.
2. Line segment: Part of a line with two endpoints.
3. Line: Undefined term.
4. Point: Undefined term.
5. Angle: A figure formed by two rays with one common initial point.
6. Acute angle: Angle whose measure is between 0° to 90°.

Here undefined terms are line and point.

All the angles of equilateral triangle are 60° each  ...(Given).

Two line segments are equal to the third-one  ...(Given).

Therefore, all three sides of an equilateral triangle are equal, because, according to Euclid’s axiom, things which are equal to the same thing are equal to one another.